Longitudinal magnons in large-$S$ easy-axis magnets

Longitudinal magnons are a distinct type of multipolar excitations in magnetic materials with large spins $S\ge 1$ and strong easy-axis anisotropy. These excitations have angular momentum $S^z = \pm 2S$ and can be viewed as a propagating full spin reversal. We study longitudinal magnons for the nearest-neighbor Heisenberg ferromagnet and antiferromagnet on a square lattice with large single-ion anisotropy. In the strong-coupling limit, we derive an effective spin-1/2 model including two leading contributions in $J/D$. The effective model provides a simple description of the longitudinal magnon dynamics. For $S=1$, we compare results from several theoretical approaches that include the effective spin-1/2 model, the linked-cluster expansion, the multiboson spin-wave theory, and, for a ferromagnet, an exact two-particle solution. Among these approaches, the multiboson spin-wave theory provides the decay rate of longitudinal magnons and describes evolution of the excitation spectra from strong to weak anisotropy.

💡 Research Summary

The paper investigates a class of magnetic excitations called longitudinal magnons (L‑magnons) that appear in large‑spin (S ≥ 1) easy‑axis magnets with strong single‑ion anisotropy D. The authors focus on the nearest‑neighbour Heisenberg model on a square lattice, both ferromagnetic (J < 0) and antiferromagnetic (J > 0), supplemented by the anisotropy term –D∑i(Si^z)^2. In the strong‑coupling limit J/D ≫ 1 the two lowest local states |±S⟩ are isolated and can be mapped onto pseudo‑spin‑½ variables. Perturbation theory in J/D yields an effective XXZ Hamiltonian for these pseudospins, \